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Simplifying 4 + -5x(x + -3) + 2x = -2 Reorder the terms: 4 + -5x(-3 + x) + 2x = -2 4 + (-3 * -5x + x * -5x) + 2x = -2 4 + (15x + -5x2) + 2x = -2 Reorder the terms: 4 + 15x + 2x + -5x2 = -2 Combine like terms: 15x + 2x = 17x 4 + 17x + -5x2 = -2 Solving 4 + 17x + -5x2 = -2 Solving for variable 'x'. Reorder the terms: 4 + 2 + 17x + -5x2 = -2 + 2 Combine like terms: 4 + 2 = 6 6 + 17x + -5x2 = -2 + 2 Combine like terms: -2 + 2 = 0 6 + 17x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -3.4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -3.4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -3.4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -3.4x + x2 = 0 + 1.2 -3.4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -3.4x + x2 = 1.2 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 1.2 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + -3.4x + x2 = 4.09 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -1.7 = 2.022374842 Simplifying x + -1.7 = 2.022374842 Reorder the terms: -1.7 + x = 2.022374842 Solving -1.7 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.022374842 + 1.7 x = 2.022374842 + 1.7 Combine like terms: 2.022374842 + 1.7 = 3.722374842 x = 3.722374842 Simplifying x = 3.722374842Subproblem 2
x + -1.7 = -2.022374842 Simplifying x + -1.7 = -2.022374842 Reorder the terms: -1.7 + x = -2.022374842 Solving -1.7 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.022374842 + 1.7 x = -2.022374842 + 1.7 Combine like terms: -2.022374842 + 1.7 = -0.322374842 x = -0.322374842 Simplifying x = -0.322374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.722374842, -0.322374842}
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